We note that in Section 3.1 of [1]} (see also [2]}) the \(infimum\)  \({d^ * }\)  for a program of the same form as the one here (the objective function is only up to a trivial \(\frac{1}{{4{G_N}}}\)  factor) has been computed directly, so we give the result directly:
\(\frac{1}{{4{G_N}}}\int _C {\sqrt{g} \lambda } \ge \frac{1}{{4{G_N}}}\sum \limits _i {Area\left( i \right)} \equiv \sum \limits _i {{S_i}}. \) 
